Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 | import type { NumberLineState } from '../../types' import { renderRollingCircle } from './renderRollingCircle' import { renderPiConstruction, mapRange } from './renderCircleConstruction' /** * Target viewport for the pi demo. * Centers the view between 0 and pi, with padding for the circle radius. */ export function piDemoViewport(cssWidth: number, cssHeight: number) { const center = Math.PI / 2 // Fit full horizontal range [-0.5, pi+0.5] = width pi+1 const ppu = Math.min((cssWidth * 0.85) / (Math.PI + 1), cssHeight * 0.35) return { center, pixelsPerUnit: ppu } } // Phase boundaries within revealProgress const CONSTRUCTION_END = 0.3 const ROLLING_END = 0.82 const ZOOM_BEGIN = 0.9 /** * Render the pi demo overlay: constructs a circle of diameter 1 from * the number line, then rolls it along the axis from 0 to pi. */ export function renderPiOverlay( ctx: CanvasRenderingContext2D, state: NumberLineState, cssWidth: number, cssHeight: number, isDark: boolean, revealProgress: number, opacity: number ): void { if (opacity <= 0) return const constructionP = mapRange(revealProgress, 0, CONSTRUCTION_END) const t = mapRange(revealProgress, CONSTRUCTION_END, ROLLING_END) const labelAlpha = mapRange(revealProgress, ROLLING_END, ZOOM_BEGIN) const zoomP = mapRange(revealProgress, ZOOM_BEGIN, 1.0) const circumColor = isDark ? '#60a5fa' : '#2563eb' const spokeColor = isDark ? '#f87171' : '#dc2626' const refColor = isDark ? 'rgba(255,255,255,0.25)' : 'rgba(0,0,0,0.15)' ctx.save() ctx.globalAlpha = opacity if (constructionP < 1) { // Construction phases: highlight → pivot → sweep → treads renderPiConstruction( ctx, state, cssWidth, cssHeight, { circumColor, spokeColor, refColor, }, constructionP, opacity ) } else { // Fade out rolling circle and labels as zoom kicks in const zoomFade = zoomP > 0 ? Math.max(0, 1 - zoomP * 3) : 1 if (zoomFade > 0.01) { // Rolling phase: circle rolls from 0 to pi const pos = renderRollingCircle( ctx, state, cssWidth, cssHeight, { radius: 0.5, circumColor, spokeColor, refColor, accentColor: isDark ? '#fbbf24' : '#d97706', trailColor: isDark ? 'rgba(255,255,255,0.2)' : 'rgba(0,0,0,0.12)', spokeLabel: '1 across', }, t, 1, opacity * zoomFade ) // === Labels === if (labelAlpha > 0) { ctx.globalAlpha = opacity * labelAlpha * zoomFade const ppu = state.pixelsPerUnit const toX = (nlx: number) => nlx * ppu - state.center * ppu + cssWidth / 2 // "pi" label at x = pi const piSx = toX(Math.PI) const fontSize = Math.max(14, Math.min(20, ppu * 0.18)) ctx.font = `bold ${fontSize}px system-ui, sans-serif` ctx.fillStyle = circumColor ctx.textAlign = 'center' ctx.textBaseline = 'top' ctx.fillText('\u03C0', piSx, pos.axisY + 8) // "one turn" annotation under pi const annoFontSize = Math.max(10, Math.min(13, ppu * 0.12)) ctx.font = `${annoFontSize}px system-ui, sans-serif` ctx.fillText('one turn', piSx, pos.axisY + 8 + fontSize + 2) // Small tick at pi ctx.beginPath() ctx.moveTo(piSx, pos.axisY - 4) ctx.lineTo(piSx, pos.axisY + 4) ctx.strokeStyle = circumColor ctx.lineWidth = 2 ctx.setLineDash([]) ctx.stroke() // "C = πd" formula above the circle const formulaFontSize = Math.max(13, Math.min(18, ppu * 0.16)) ctx.font = `${formulaFontSize}px system-ui, sans-serif` ctx.fillStyle = isDark ? 'rgba(255,255,255,0.9)' : 'rgba(0,0,0,0.8)' ctx.textAlign = 'center' ctx.textBaseline = 'bottom' ctx.fillText('C = \u03C0d', pos.ccx, pos.ccy - pos.screenR - 8) // "trip around ÷ distance across" subtitle const subFontSize = Math.max(10, Math.min(13, ppu * 0.11)) ctx.font = `${subFontSize}px system-ui, sans-serif` ctx.fillStyle = isDark ? 'rgba(255,255,255,0.6)' : 'rgba(0,0,0,0.5)' ctx.fillText( 'trip around \u00F7 distance across', pos.ccx, pos.ccy - pos.screenR - 8 - formulaFontSize - 2 ) } } } // === Irrationality zoom (final phase) === // The actual number-line viewport zoom is driven by useConstantDemo. // Here we just overlay a floating decimal expansion at the top of the screen. if (zoomP > 0) { const fadeIn = zoomP < 0.25 ? zoomP * 4 : 1 const smoothFadeIn = fadeIn * fadeIn * (3 - 2 * fadeIn) // Decimal expansion typing out const decimalStr = '3.14159265358\u2026' const charsToShow = Math.min(decimalStr.length, Math.floor(1 + zoomP * (decimalStr.length - 1))) const displayText = '\u03C0 = ' + decimalStr.substring(0, charsToShow) const fs = Math.max(16, Math.min(24, cssWidth * 0.03)) ctx.font = `bold ${fs}px system-ui, monospace` ctx.fillStyle = circumColor ctx.textAlign = 'center' ctx.textBaseline = 'top' ctx.globalAlpha = opacity * smoothFadeIn ctx.fillText(displayText, cssWidth / 2, 20) // Subtitle if (zoomP > 0.7) { const neverP = zoomP < 0.9 ? (zoomP - 0.7) / 0.2 : 1 const smoothNP = neverP * neverP * (3 - 2 * neverP) const subFs = Math.max(11, Math.min(15, cssWidth * 0.02)) ctx.font = `italic ${subFs}px system-ui, sans-serif` ctx.fillStyle = isDark ? 'rgba(255,255,255,0.6)' : 'rgba(0,0,0,0.5)' ctx.textAlign = 'center' ctx.textBaseline = 'top' ctx.globalAlpha = opacity * smoothNP * 0.8 ctx.fillText('The digits never end!', cssWidth / 2, 20 + fs + 6) } } ctx.globalAlpha = 1 ctx.setLineDash([]) ctx.restore() } |